Homogenization of the Schrodinger equation with a time oscillating potential

We study the homogenization of a Schrodinger equation in a periodic medium with a time dependent potential. This is a model for semiconductors excited by an external electromagnetic wave. We prove that, for a suitable choice of oscillating (both in time and space) potential, one can partially transfer electrons from one Bloch band to another. This justifies the famous "Fermi golden rule" for the transition probability between two such states which is at the basis of various optical properties of semiconductors. Our method is based on a combination of classical homogenization techniques (two-scale convergence and suitable oscillating test functions) and of Bloch waves theory

Protecting America\u27s Elections from Foreign Tampering: Realizing the Benefits of Classifying Election Infrastructure as Critical Infrastructure under the United States Code

In just the past five years, the United States has suffered numerous hacks into important entities and institutions across the country by ill-intentioned actors. Private companies and government agencies alike have felt the negative impacts of security breaches by hackers infiltrating proprietary and protected systems. Even the United States political landscape has proven vulnerable to bad actors in the realm of cyber security. Furthermore, analysts have attributed some of the most recent highly publicized hacks to state-sponsored groups. As cyber security threats and opportunities for foreign hackers to infiltrate critical systems become more prevalent, it is natural to wonder where the next hack will occur, when it will happen, and whom it will affect. This comment concludes that the critical infrastructure classification for election infrastructure will help thwart potential state-sponsored threats to American election legitimacy

Periodic homogenization of a pseudo-parabolic equation via a spatial-temporal decomposition

Pseudo-parabolic equations have been used to model unsaturated fluid flow in porous media. In this paper it is shown how a pseudo-parabolic equation can be upscaled when using a spatio-temporal decomposition employed in the Peszyn'ska-Showalter-Yi paper [8]. The spatial-temporal decomposition transforms the pseudo-parabolic equation into a system containing an elliptic partial differential equation and a temporal ordinary differential equation. To strengthen our argument, the pseudo-parabolic equation has been given advection/convection/drift terms. The upscaling is done with the technique of periodic homogenization via two-scale convergence. The well-posedness of the extended pseudo-parabolic equation is shown as well. Moreover, we argue that under certain conditions, a non-local-in-time term arises from the elimination of an unknown.Comment: 6 pages, 0 figure

Digital control of magnetic bearings supporting a multimass flexible rotor

The characteristics of magnetic bearings used to support a three mass flexible rotor operated at speeds up to 14,000 RPM are discussed. The magnetic components of the bearing are of a type reported in the literature previously, but the earlier analog controls were replaced by digital ones. Analog-to-digital and digital-to-analog converters and digital control software were installed in an AT&T PC. This PC-based digital controller was used to operate one of the magnetic bearings on the test rig. Basic proportional-derivative control was applied to the bearings, and the bearing stiffness and damping characteristics were evaluated. Particular attention is paid to the frequency dependent behavior of the stiffness and damping properties, and comparisons are made between the actual controllers and ideal proportional-derivative control

A magnetic damper for first mode vibration reduction in multimass flexible rotors

Many rotating machines such as compressors, turbines and pumps have long thin shafts with resulting vibration problems, and would benefit from additional damping near the center of the shaft. Magnetic dampers have the potential to be employed in these machines because they can operate in the working fluid environment unlike conventional bearings. An experimental test rig is described which was set up with a long thin shaft and several masses to represent a flexible shaft machine. An active magnetic damper was placed in three locations: near the midspan, near one end disk, and close to the bearing. With typical control parameter settings, the midspan location reduced the first mode vibration 82 percent, the disk location reduced it 75 percent and the bearing location attained a 74 percent reduction. Magnetic damper stiffness and damping values used to obtain these reductions were only a few percent of the bearing stiffness and damping values. A theoretical model of both the rotor and the damper was developed and compared to the measured results. The agreement was good

BOOK REVIEWS

The Politics of Justice: Lower Federal Judicial Selection and the Second Party System - Book Author: Kermit L. Hall; Book Reviewed by Lawrence M. Friedman In The Politics of Justice, Kermit L. Hall, a history professor at Wayne State University, takes a look at the way Presidents from Jackson through Buchanan picked judges for the federal district courts and for the territories. There were 240 such appointments during the period studied... There is something of a literature on the selection process, although Hall\u27s book does fill a rather glaring hole. The tale Hall tells rings true if we ignore a few overripe conclusions... We have activist courts, and an intensely political way of choosing judges. These two aspects of American law are certainly not unrelated. They fit each other like hand and glove. Through along, intricate historical dance of fate, they have become totally intertwined, and are now inseparable. How this came about and grew is an important part of our history, and The Politics of Justice makes a definite contribution to the telling. Must Corporate Income Be Taxed Twice? - Reviewed by Allaire Urban Karzon This study by Charles E. McLure, Jr. originated from a 1977 conference at the Brookings Institution,\u27 which focused on the technical and administrative problems that would be encountered if this country were to integrate in any form the corporate and individual income taxes. Must Corporate Income Be Taxed Twice? is a feasibility study of integration in practice, not a policy evaluation of the social desirability of integration... Before closing, some minor flaws in the book must be mentioned. Parts of its analysis are needlessly repetitive. McLure\u27s style is not crisp. There is not sufficient recognition of the criticism, expressed mainly by the legal profession, that the proposed tax reforms discussed by McLure would introduce great and perhaps unjustified complexity to the Internal Revenue Code.\u27 To some, reforms that are comprehensible only to technicians are not reforms. To some, simplification of the tax laws and certainty of consequences for taxpayers are objectives greatly to be desired... McLure\u27s review of the major questions that remain unanswered relating to the shareholder credit method, especially in the international context, leads to the inescapable inference that its adoption at this time would be premature. There are too many pitfalls that an uninformed, precipitous legislative move could unwittingly create

Microgravity vibration isolation: An optimal control law for the one-dimensional case

Certain experiments contemplated for space platforms must be isolated from the accelerations of the platforms. An optimal active control is developed for microgravity vibration isolation, using constant state feedback gains (identical to those obtained from the Linear Quadratic Regulator (LQR) approach) along with constant feedforward (preview) gains. The quadratic cost function for this control algorithm effectively weights external accelerations of the platform disturbances by a factor proportional to (1/omega)(exp 4). Low frequency accelerations (less than 50 Hz) are attenuated by greater than two orders of magnitude. The control relies on the absolute position and velocity feedback of the experiment and the absolute position and velocity feedforward of the platform, and generally derives the stability robustness characteristics guaranteed by the LQR approach to optimality. The method as derived is extendable to the case in which only the relative positions and velocities and the absolute accelerations of the experiment and space platform are available

Smoluchowski-Kramers approximation in the case of variable friction

We consider the small mass asymptotics (Smoluchowski-Kramers approximation) for the Langevin equation with a variable friction coefficient. The limit of the solution in the classical sense does not exist in this case. We study a modification of the Smoluchowski-Kramers approximation. Some applications of the Smoluchowski-Kramers approximation to problems with fast oscillating or discontinuous coefficients are considered.Comment: already publishe